Exploring Dynamical Systems: Exposing Students to Contemporary Mathematics

Trustees Of Boston University, Boston

Investigators

Abstract

One of the major difficulties facing mathematics today is the fact that most people have no idea about what is happening in contemporary mathematics or why this field is important. Unfortunately, most contemporary research in this field is difficult, if not impossible, to explain to students. The problem is that much of today's mathematics builds upon years or even centuries of prior mathematical research. As a consequence, undergraduate students rarely have the background to experience what is new and exciting in this field. In this project, the PI and his collaborators are attempting to change this culture by creating a series on on-line activities that provide students with the background and the tools necessary to experience and investigate certain contemporary topics in mathematics. The activities are drawn from the areas of mathematics known as dynamical systems theory and fractal geometry. These are two relatively new areas of mathematics that have widespread applicability in all areas of science and engineering. In addition, much of the current research in this field involves a significant experimental component involving computer graphics. Most importantly, much of the PI's current research in these areas involves iteration of simple expressions (such as quadratic functions), and so many of the ideas in this field can be readily explained to students with only a high school background in mathematics. In this project, the PI is developing a series of ten stand-alone modules, each of which is designed to acquaint the user with a particular topic of interest in these fields. Each module includes streaming video introductions, online software (java applets), computer generated animations, and suggested areas for student investigation. The materials being developed can be woven into courses throughout the curriculum, ranging from introductory math courses for liberal arts students and precalculus to calculus and linear algebra courses, to give students an ongoing glimpse of the excitement of modern mathematics. Alternatively, the modules can be concatenated in a string of activities designed to bring the student to the forefront of active research in this area.